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Non-Routine Questions 2
Notes
Heuristics: Working Backwards
The strategy of working backwards only applies to a specific type of
mathematical word problems. Such mathematical word problems state the
end result. Therefore, in order to solve these mathematical word problems, the
students have to work backwards through the sequence of events beginning
with the end result given.
The strategy of working backwards allows students to use their logical
reasoning and sequencing to find the answers to the mathematical word
problems.
Below are some examples of mathematical word problems that can be solved
using this strategy.
1. Calvin spent 10 minutes eating his lunch immediately after reaching home.
He spent another 10 minutes bathing. After that, Calvin spent 2 hours 15
minutes doing his homework. He completed his homework at 3.55 pm. At
what time did he have his lunch?
2. Betty has a piece of ribbon. She cuts the ribbon into 4 equal pieces. Each
piece is then cut into 3 smaller equal pieces. The length of each small
piece is 35 cm. How long is the piece of ribbon?
3. Mrs Field had some money. She bought three chickens for $15 and 3 kg
of potatoes at $1.55 per kilogram. After buying some fruit for $9, she had
$37 left. How much money did she have at first?
_1_
4. Rick, Henry and Daniel were given some chocolate bars. Rick took the
2
_1_
total number of chocolate bars. Henry took of the remaining chocolate
4
bars and Daniel took 33 chocolate bars. There were 12 chocolate bars
left. How many chocolate bars were given to the three boys?
Learning Maths Book 3
© Singapore Asia Publishers Pte Ltd. All rights reserved.
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE. Non-Routine Questions 2Do these questions on another piece of paper.
. Millie bought a badminton racket that cost $29.90. She gave the
shopkeeper the exact amount with 5 pieces of dollar notes and 3
coins. What were the dollar notes and coins she had given to the
shopkeeper?
. A garden is situated in the centre of Jamie’s house and her school.
The distance between the garden and her school is 1 km. What is
the distance from Jamie’s house to her school?
3. Replace the following letters with digits 1, 2, 3 and 4. The addition
of AB and CD is 46. The addition of DC and BA is 64. Find the
digits that represent letters A, B, C and D.
4. Plant A is 1 m tall. Plant B is 50 cm taller than Plant A. Plant C is
5 cm shorter than Plant A. What is the total height of the tallest
and the shortest plants?
5. Mr Robinson took a flight from Singapore to Tokyo, Japan. The
flight was 7 hours. The time in Tokyo is an hour faster than the
time in Singapore. If Mr Robinson reached Tokyo at 7 am on 14
September, find the time of his flight in Singapore.
1
__
6. Grace dropped a string into a measuring cylinder of oil and water.
4
1
__
of the string was immersed in oil and water. of the string was
8
immersed in water. If 5 cm of the string was immersed in water,
what was the total length of the string?
7. Ken has 3 pieces of dollar notes. The first piece of dollar note is
twice the amount of money of the second one. The third piece of
dollar note is ten times the amount of money of the second one.
The difference between the largest and the smallest amounts is
$45. How much money does Ken have?
Learning Maths Book 3
© Singapore Asia Publishers Pte Ltd. All rights reserved.
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE. Non-Routine Questions 28. The time in New York is 12 hours slower than the time in Singapore.
What will be the time in New York when the clock strikes twelve
midnight on Christmas Day in Singapore?
1 1
__ __
9. Simon’s father ate of a pizza. Simon ate of what his father
2 2
1
__
had eaten. Simon’s mother ate of what Simon had eaten. The
2
remaining 2 pieces of pizza were eaten by Simon’s brother. How
many pieces of pizza were there at first?
0. Mrs Davis bought a fish at a market. She gave the stall-owner $50.
She received the change in 4 pieces of dollar notes in two different
denominations. One of the dollar notes was 5 times the amount of
money of the other dollar note. The change was between $20 and
$25. How much was the fish?
. A bean plant grows 1 cm every three days. How long will the bean
plant grow after 30 days?
. Study the numbers carefully. Find the missing number.
118 159 277
269 ? 623
387 513 900
Learning Maths Book 3
© Singapore Asia Publishers Pte Ltd. All rights reserved.
3
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE. Non-Routine Questions 2
